Cross-sample entropy estimation for time series analysis: a nonparametric approach

Cross-sample entropy (CSE) allows to analyze the association level between two time series that are not necessarily stationary. The current criteria to estimate the CSE are based on the normality assumption, but this condition is not necessarily satisfied in reality. Also, CSE calculation is based on a tolerance and an embedding dimension parameter, which are defined rather subjectively. In this paper, we define a new way of estimating the CSE with a nonparametric approach. Specifically, a residual-based bootstrap-type estimator is considered for long-memory and heteroskedastic models. Subsequently, the established criteria are redefined for the approach of interest for generalization purposes. Finally, a simulation study serves to evaluate the performance of this estimation technique. An application to foreign exchange market data before and after the 1999 Asian financial crisis was considered to study the synchrony level of the CAD/USD and SGD/USD foreign exchange rate time series. A bootstrap-type method allowed to obtain a more realistic estimation of the cross-sample entropy (CSE) statistics. Specifically, estimated CSE was slightly different than that obtained in previous studies, but for both periods the synchrony level using CSE between the time series was higher after the 1999 Asian financial crisis.